## Thursday, February 7, 2008

### IIT JEE Physics Formula Revision 42. Photoelectric Effect and Waveparticle Duality

1. Relation between properties of photon and properties of light waves.

E and p are energy and linear momentum of a photon of light.
ν and λ are the frequency and wavelength of the same light when it is considered (behaves) as a wave.

Then E = hν = hc/λ
p = h/λ = E/c ... (42.1)

wherein h is a universal constant known as the Planck constant and has a value 6.626*10^-34 J-s and is also equal to 4.136*10^-15 eV-s.

C = velocity of light vacuum = 299,792,458 m/s ≈ 3.0*10^8 m/s

2. The maximum kinetic energy of the electron that comes out due to energy E supplied is:

Kmax = E – φ

Some energy from the E – φ is dissipated as the electron may have some collision before escaping from the material.

If monochromatic light of wave length is incident on the metal surface, photons of energy hc/ λ fall on the surface. The maximum kinetic energy of an electrons that comes out due to these photons is:

Kmax = hc/λ - φ = h υ - φ

The above equation is called Einstein's photoelectric equation.

3. Writing work function φ as hυ0 (h multiplied by frequency)

υ λ = c
υ0 = c/ λ0
λ0 = threshold wavelength

Kmax = h(υ - υ0)

4. Relation between Maximum kinetic energy of photoelectrons and stopping potential:

As a photoelectron travels from the cathode to the anode, the potential energy increases by eV0. This is equal to the decrease in the kinetic energy of the photoelectron.

The maximum kinetic energy a photoelectron will have is hc/λ - φ
Hence eV0. = hc/λ – φ

V0 = hc/e(1/ λ) – φ/e

5. A relation for wavelength of electron was proposed by Louis Victor de Broglie.

The proposed expression for wavelength is

λ = h/p

Where p is the momentum of the electron and
h is the Planck constant.